Clasificación del álgebra de Lie, leyes de conservación y soluciones invariantes para un caso particular de la ecuación generalizada e Levinson-Smith


Autores/as

DOI:

https://doi.org/10.22517/23447214.24960

Palabras clave:

Soluciones Invariantes, Grupo de simetrías de Lie, Sistema Optimo, Clasificación del álgebra de Lie, Simetrías variacionales, Leyes de Conservación, Teorema de Noether

Resumen

En este estudio, examinamos una instancia específica de la ecuación generalizada de Levinson-Smith, que está vinculada con la ecuación de Liènard y tiene una gran importancia desde las perspectivas de la física, las matemáticas y la ingeniería. Esta ecuación subyacente tiene aplicaciones prácticas en mecánica y dinámica no lineal, y ha sido ampliamente explorada en el esquema cualitativo. Nuestro enfoque implica aplicar el método de grupos de Lie a esta ecuación. Al hacerlo, obtenemos los operadores generadores óptimos del sistema que se refieren a la instancia específica de la ecuación generalizada de Levinson-Smith. Luego, se utilizan estos operadores para definir todas las soluciones invariantes asociadas con la ecuación. Además, demostramos las simetrías variacionales y las leyes de conservación correspondientes utilizando el teorema de Noether. Finalmente, categorizamos el álgebra de Lie relacionada con la ecuación dada.

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Publicado

2023-06-30

Cómo citar

Acevedo Agudelo, Y. A., Loaiza Ossa, G. I., Londoño Duque, O. M. ., & García Hernández, D. A. . (2023). Clasificación del álgebra de Lie, leyes de conservación y soluciones invariantes para un caso particular de la ecuación generalizada e Levinson-Smith. Scientia Et Technica, 28(02). https://doi.org/10.22517/23447214.24960

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